Mathematics - Quadratic Equation Question with Solution | TestHub

Given equation can be written as $\left(x^2-3x+3\right)-f=O$ where $f=x-[x]$ and $O\le f<1$ $\therefore O\le x^2-3x+3<1$ solving $x^2-3x+3=O$; roots are Imaginary $\therefore x^2-3x+3\ge O\forall x\in R$ solving $x^2-3x+3<1\Rightarrow 1<x<2$ if $1<x<2;[x]=1$. putting $[x]=1$ in the given equation and solving we get $x=2$. But $1<x<2\therefore$ the given equation has no solution.